A Coupled Model of Soil-Plant-Atmosphere Based on the Stomatal Optimization for C4 Crops.

It has been conjectured that the C4 photosynthetic pathway in plants evolved in response to declining atmospheric CO₂ concentrations. At low CO2 concentrations, the assimilation in C₄ plants can sustain high rates of photosynthesis at low stomatal conductance and reduced transpiration thereby offering clear advantages over C₃ plants. Despite this unique response of C₄ plants to  environmental conditions, stomatal conductance of these plants has been mostly treated as resembling their C₃ counterparts in crop models thereby challenging their application to future climatic conditions. The aim of this study is to introduce an approach to implement an optimization theory of stomatal conductance into a dynamic canopy gas exchange model for C₄ plants. Two key leaf-level variables in this theory are required above and beyond what is commonly formulated for C₃ species.  The first is the efficiency of the CO₂-concentrating mechanism known as the C₄ pump, and the second is  the so-called marginal water use efficiency (MWUE). Both parameters are assumed to be constant on time scales commensurate with fluctuations in stomatal aperture. However, on time scales relevant to crop productivity (daily to seasonal), the boundary conditions on the optimization problem evolve in time prompting the question of how to assign MWUE on such time scales and what is precisely its connection to the C₄ pump. To address this question, MWUE was first formulated independent of the C₄ pump as a function of time-integrated leaf-water potential. Next, leaf water potential was linked to root and soil pressure using a soil water balance model based on a modified Richards' equation that considers vertical distribution of root water uptake. The adequacy of the new approach was tested by comparing predicted diurnal cycles of assimilation and transpiration as well as variability of soil moisture with long-term eddy-covariance observations at two agricultural plots in southwest Germany cultivated with two maize cultivars.